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metric_space [2014/11/20 12:59]
nikolaj
metric_space [2015/01/21 19:41] (current)
nikolaj
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 | @#55EE55: postulate ​  | @#55EE55: $d$ ... metric $X$ | | @#55EE55: postulate ​  | @#55EE55: $d$ ... metric $X$ |
  
-==== Discussion ====+-----
 We can reconstruct the set underlying a metric via $\text{dom}(\text{dom}(d))=\text{dom}(X\times X)=X$, so the set of metrics and the set of metric spaces over $X$ are in bijection. We can reconstruct the set underlying a metric via $\text{dom}(\text{dom}(d))=\text{dom}(X\times X)=X$, so the set of metrics and the set of metric spaces over $X$ are in bijection.
 === Reference === === Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Metric_space|Metric space]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Metric_space|Metric space]]
-==== Parents ==== + 
-=== Refinement of === +-----
-[[Hausdorff space]]+
 === Requirements* === === Requirements* ===
 [[Metric]] [[Metric]]
 +=== Refinement of ===
 +[[Hausdorff space]]
 === Equivalent to === === Equivalent to ===
 [[Metric]] [[Metric]]
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